Page 1 of 3 Source: College Mathematics , Rockswold G., Bennett J., and Briggs W. C:/CLASES_COLEGIO/2007/NOTAS/0102/ 02/13/07 Math 1332 - College Mathematics Chapter 5-4 Notes Logarithmic Functions and Models We learned how to solve linear and quadratic equations, we now solve for exponential equations of the form a = k x , where the variable x is an exponent. We introduce logarithmic functions, which model data that grows much at a slower pace than exponential functions. Logarithmic functions can be used to solve exponential equations. Base-a Logarithms Logarithm : The logarithm with base a of a positive number x , is defined as log a x = k if and only if x = a k , where a > 0, a ≠ 1, and k is a real number. f(x) = log a x Æ is the Logarithmic Function with base a Note Æ A logarithm is an exponent ( k ) Inverse Properties of Logarithm : • log a a x = x for a any real number x • a log a x = x for any positive number x Ex: log 3 9 log ¼ 64 Graph of y = log a x Æ • always passes through the point (1,0) since

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